A rectanglular box without a front and without a bottom is to be built. The volume of the box equals 16 cubic feet. Find the dimensions [ X, Y, Z ] of the box that will minimize the surface area.

Q: A box with an open top and a square base is to be constructed with a volume of 32, 000 cm^3. Find…

A: Given, Square base, Therefore, l=b=x Let height be h. Therefore, Volume= lbh =x²h Given, Volume=…

Q: A box with a square base and open top must have a volume of 32m3. Find the dimensions of the boxthat…

A: Given,  V=32 m3                                      ..........................(1) The amount of…

Q: Draw the given optimization problem and solve. Find the dimensions of the closed cylinder volume…

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Q: The base of an aquarium with given volume V is made of slate and the sides are made of glass. If…

A: We need to minimize cost.

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Q: A closed box with a square base is to have a volume of 2000 cm3. the material for the top bottom of…

A: Let x be the length and width and y be the height of the box. Calculate the area of the top, bottom…

Q: The packaging department in a company is to design a rectangular box with no top and a partition…

A: Given,    The volume of rectangular box is 48 cubic inches.

Q: The base of a rectangular prism shaped aquarium without a lid is made of slate and the sides are…

A: Given Volume of the tank V=96 m3 Cost of slate (S) = 3 Cost of Glass (G) (per unit area) S=3G

Q: An open-topped box is to be constructed with a base whose length is twice its width. The material…

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Q: A cylindrical drum is to be manufactured from a synthetic material and is to hold 547 m³ of liquid.…

A: The solution is given below in the next step:

Q: a box with a square base and an open top must have a volume of 4000 cm^3. find the dimensions of the…

A: Let the length of each side of the base= x Height=y So

Q: A rectangular box is to have a square base and a volume of 63 ft3. If the material for the base…

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Q: A box with a square base has a volume of 3375 ft3 . Find the dimensions of the box that minimize the…

A: It's given that the box has a square base. However, nothing is said about the the height.  Let the…

Q: A large container in the shape of a rectangular solid must have a volume of 480 m3. The bottom of…

A: A large container in the shape of a rectangular solid must have a volume of 480 m3. The bottom of…

Q: A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the…

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Q: Q2. Use the Method of Lagrange Multipliers to find the dimensions of the closed right circular…

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Q: A rectangular storage container with a square base and an open top is to have a fixed volume of…

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Q: A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the…

A:

Q: A box without a lid is required to have volume, V = 32000 cm^3. Minimize the amount of cardboard…

A:

Q: A closed box with a square base is to have a volume of 2000 cm3. The material for the top and bottom…

A: closed box with a square base is to have a volume of = 2000 cm3.  Assume x be the side of the top…

Q: Hi, I am wondering how to do the work for this problem and what the final answer would be. Thank you

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Q: A box with a square base and open top must have a volume of 512 cubic inches. Find the dimensions of…

A: The solution is given below:

Q: A box with a square base and a closed top has a volume of 20 cubic ft. the cost of material for the…

A: Given:     Volume of square base = 20 cubic feet.…

Q: A Box with a Square base and an open Top must have a volume of 500 cm'. Find the dimensions of the…

A: A box with a square base and an open top must have a volume of 500 cm. To find: The dimensions of…

Q: A box with a square base and open top must have a volume of 32,000 cm3. Find the dimensions of the…

A:

Q: Find the dimensions of a cylinder of volume 1 m 3of minimal costif the top and bottom are made of…

A: Given: Find the dimensions of a cylinder of volume 1 m 3of minimal cost if the top and bottom are…

Q: A cardboard box without a lid is to have a volume of 32,000 cubic centimeters. Find the dimensions…

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Q: A box with a square base and an open top must have a volume of 32,000 cubic centimeters. Find the…

A: let x denotes the length of the sides on the square base assume height of the box is h   Then the…

Q: Suppose you are designing a rectangular room with a fixed perimeter of 60 ft, use the method of…

A: Consider the equation

Q: What should the dimensions of the box be in order to minimize the surface area?

A: Let,Breadth of the box = b = xLength of the box = l = 2b = 2x        (according to question)Height…

Q: An open-top rectangular box is being constructed to hold a volume of 350 in. The base of the box is…

A: Given :  an open top rectangular box is being constructed to hold a volume of 350 in3, the base of…

Q: A box with a volume of 15 m³ is to be constructed with a gold-plated top, silver-plated bottom, and…

A:

Q: the base of an aquarium with given volume V is made of slate and the sides are made of glass. if the…

A:

Q: A large container in the shape of a rectangular solid must have a volume of 480 m3. The bottom of…

A: Assume that the length, width, and height of the rectangular solid be x, y, and z respectively.…

Q: Please solve and explain q#4.

A: Let x be the height , y and z be the dimensions of base of rectangular box, then volume is…

Q: The volume of a box without a top is 36 m3, where the length is twice of width. Find the dimensions…

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Q: A manufacturing company is responsible for designing a can for diced tomatoes which will have a…

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Q: A box with a volume of 512cm3 is to be constructed. The sides of the box cost 2 cents per cm2, and…

A: Given the volume of the box is

Q: As a petrochemical engineer, you are required to design a conical container (without a cover) to…

A: The shape of the container is conical, so, the surface area of the container will be S=πrr2+h2,…

Q: A closed rectangular box with square base is to be constructed. Suppose the volume is 27 cubic cm.…

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Q: I will accept a package whose combined height and perimeter of the base are at most 140 inches. Use…

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Q: We wish to empty a hemispherical tank full of water out the top. Which should entail the larger…

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Q: A closed top storage box with a square base has capacity of 64 m'. Find the dimensions that will…

A: A closed-top storage box with a square base has a capacity of 64 m3. We have to find the dimensions…

Q: A carpenter wants to build a rectangular box with square top and bottom. The material for the bottom…

A:

Q: A net enclosure for practising golf shots is open at one end, as shown. Find the dimensions that 3)…

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Q: Find the dimensions of a open topped box that maximizes the volume with the constraint that the…

A: We will use Lagranges multiplier method to find dimension of the box .